Method for bispectral picking of anelliptical nmo correction parameters

ABSTRACT

Method of determining the velocity V and anellipticity η parameters for processing seismic traces in a common midpoint (CMP) gather comprising:—a preliminary step to define a plurality of nodes (dtn, τ o ), for each node (dtn, τ o ) defined in the preliminary step, the following steps:—for static NMO correction of traces in the CMP gather as a function of the values of the said parameters dtn and τ o  at the node considered, and calculation of the semblance function associated with the said NMO correction for the node considered; and—for each picked time t o , a step including determination of the maximum semblance node (dtn (t o ), τ o  (t o )),—and a final step to convert the dtn (t o ) and τ o  (t o ) parameters, so as to obtain the velocity t o ) and anellepticity η (t o ) laws.

The field of this invention is seismic prospecting. The invention relates particularly to processing of seismic traces in a common midpoint gather.

The invention is more precisely related to a method of determining velocity V and anellipticity η parameters necessary to perform processing including NMO correction of seismic traces.

Seismic prospecting usually consists of emitting seismic waves in the subsoil using one or several seismic sources, and making surface records of seismic data corresponding to seismic waves reflected on geological interfaces in the subsoil as a function of time (also called reflectors) using receivers (also called geophones or hydrophones) depending on whether the prospecting is being done on land or at sea) and then processing these data to extract useful information about the geology of the subsoil.

The record of the seismic energy produced by each receiver during data acquisition is called a seismic trace.

One conventional technique for seismic prospecting is multiple coverage, in which sources and receivers are arranged such that several seismic traces are grouped together at the same midpoint (in other words the point at equal distance between the source and the receiver for a given trace).

Although seismic traces contain useful information about seismic reflections and geology of the subsoil, they also contain noise components.

One of the first purposes of the processing of seismic data is to eliminate, or at least attenuate, these unwanted noise components such that the useful information can be clearly identified and interpreted.

One conventional method used to attenuate these noise components is Common MidPoint (CMP) gather. Traces with the same midpoint are then grouped as a function of the distance between the source and the receiver (called the offset).

In general, representation of seismic data in images requires the use of processing including:

-   -   a so-called TZO (Transform to Zero Offset) operation designed to         compensate for the NMO effect of paths by correcting the arrival         time of reflections to the arrival time of traces with zero         offset,     -   and a migration operation designed to reproduce the correct         shapes of the geological interfaces.

Although these TZO and migration operations are usually carried out one after the other, they can be carried out jointly. This is the case particularly when a time migration is done before stack (PSTM—Pre-Stack Time Migration).

In a simplified manner, the TZO operation simulates acquisition of seismic data by sources and receivers placed at the common mid-point.

The purpose is to add records illuminating the same point in the subsoil to increase the signal to noise ratio and the primary reflections to secondary reflections ratio, and thus benefit from the advantages of “multiple coverage”.

In order to make a zero offset image, a so-called obliqueness correction method or NMO (Normal Move Out) correction method is used.

If it is assumed that the subsoil is horizontally stratified with no lateral variation of the propagation velocities, it can be shown that records that have the property of illuminating the same point in the subsoil are records that have the same midpoint.

However, the image of a reflection in the subsoil arrives at variable times depending on the offset. Therefore, in order to stack reflections, it is necessary to start by correcting the various records to bring them all to a common zero offset reference.

Historically, the NMO correction is based on a particularly simple model of the subsoil; a homogeneous model with horizontal reflectors.

In this model, reflections associated with each subsoil reflector are theoretically aligned along hyperbolas also called indicators, centred vertically above the midpoint.

The arrival time of a reflection is then a hyperbolic function of the source-receiver offset, the shortest time being obtained at zero offset.

In order to stack records in each gather, the NMO correction straightens the hyperbolas until they are theoretically horizontal.

The NMO correction is then made based on the following hyperbolic equation for the travel time t after reflection, associated with a source-receiver offset x pair: $t^{2} = {t_{0}^{2} + \left( \frac{x}{V} \right)^{2}}$ in which t₀ represents the zero offset travel time and V denotes the average propagation velocity of waves in the subsoil.

The simplistic model mentioned above is based particularly on assumptions such as low angles of incidence and an isotropic medium.

But assumptions made for the simplistic model are too restrictive to describe a complex medium, and in particular cannot be applied to the propagation of seismic waves in an anisotropic medium (medium in which the velocity of waves can vary depending on the propagation direction).

The use of a less simplistic model is necessary, particularly due to:

-   -   the use of long streamers for acquisition in deep offshore,         which in particular means that traces with far offsets are         acquired;     -   observation of anisotropy in clayey type sediments.

The generally accepted assumption consists of modelling an anisotropic medium as a stack of transversely isotropic layers with a vertical axis of symmetry. This is known as Vertical Transverse Isotropy (VTI).

Thus, it has been proposed to determine NMO corrections to be made by:

-   -   introducing vertical non-homogeneity into a homogenous VTI         medium model, as presented in the document “ALKHALIFAH T. and         TSVANKIN I., 1995, Velocity analysis for transversely isotropic         media: Geophysics, 60, 1550-1566”;     -    or by     -   introducing VTI anisotropy into a model with stratified         isotropic layers, as demonstrated in document “SILIQI R. and         BOUSQUIE N., 2000, Anelliptic time processing based on an offset         hyperbola approach, 70^(th) Ann. Internat. Mtg.: Soc. Of Expl.         Geophys., 2245-2248”.

This second approach combining vertical non-homogeneity and VTI anisotropy to give a new model of the subsoil, appears to be the best approach in most real cases studied.

The following equation for correction of the travel time t after reflection, using an anelliptic offset hyperbola, associated with a source—receiver offset x pair, is derived from this model: $\begin{matrix} {{t\left( {V,\eta} \right)} = {{\frac{8\quad\eta}{1 + {8\quad\eta}}t_{0}} + \sqrt{\left( \frac{t_{0}}{1 + {8\quad\eta}} \right)^{2} + \frac{x^{2}}{\left( {1 + {8\quad\eta}} \right)V^{2}}}}} & {{Equation}\quad\left( {1a} \right)} \end{matrix}$ where V is the velocity conventionally used in seismic corresponding to small offsets and η is a parameter, called the anellipticity parameter.

The document “SUAUDEAU E. and SILIQI R., 2001, Anelliptic pre-stack time migration, Annual International Meeting, CSEG Expanded Abstracts” also proposes to include the NMO correction by anelliptic offset hyperbola in the equation for the path time used during the PSTM migration operation.

The PSTM migration equation is conventionally expressed in the form of a double anelliptic offset hyperbola, which is the sum of two square roots (the Double Square Root (DSQR) equation).

Taking account of anellipticity, the expression for this constant offset equation, becomes: $\begin{matrix} \begin{matrix} {t = {{\frac{8\quad\eta}{1 + {8\quad\eta}}t_{0}} + \sqrt{\left( \frac{t_{0}/2}{1 + {8\quad\eta}} \right)^{2} + \frac{\left( {x - x_{m} + h} \right)^{2}}{\left( {1 + {8\quad\eta}} \right)V^{2}}} +}} \\ {\sqrt{\left( \frac{t_{0}/2}{1 + {8\quad\eta}} \right)^{2} + \frac{\left. {x - x_{m} - h} \right)^{2}}{\left( {1 + {8\quad\eta}} \right)V^{2}}}} \end{matrix} & {{Equation}\quad\left( {1b} \right)} \end{matrix}$

where:

-   -   the V and η parameters are those mentioned above,     -   x_(m) is the coordinates of the midpoints,     -   x−x_(m) represents the migration aperture,     -   h is the half source-receiver offset,     -   t₀ is the double time for zero aperture of the operator.

Note that when the aperture x−x_(m) of the migration is zero, the PSTM correction equation (1b) becomes the NMO correction equation (1a). Thus, the NMO correction forms a special case of the PSTM migration; the case of PSTM migration with zero aperture.

Therefore, finally, in order to perform seismic data processing including NMO correction taking account of vertical heterogeneity and VTI type anisotropy, it is necessary to determine the velocity V and anellipticity η parameters.

The said parameters V and η can conventionally be estimated by carrying out two passes such that:

-   -   during the first pass, the distribution of velocities V along         the time axis is estimated, only using data with near offsets;     -   during the second pass, the anellipticity η is estimated along         the time axis, using:     -   the distribution of velocities determined during the first pass,         and     -   all data (including data with far offsets).

The document entitled:

“SILIQI R. 2001, Technological leap in time processing focuses the data throughout anisotropic media: First Break, .19, No.11, 612-618”, has also demonstrated that the parameters V and η can be estimated in a single pass, during which bispectral analyses are carried out in order to simultaneously pick the V and η parameters along the time axis, using all data.

However, dense analyses of NMO correction parameters are preferably made when the correction equation no longer depends on the time t₀ (we then talk about static NMO correction).

A static correction effectively provides a means of offsetting all samples each forming traces of the same time δt, for a given offset.

Thus, when a static correction is made, the number of calculations to be made can be significantly reduced and the trace stretching phenomenon is eliminated, which makes the said dense analyses viable.

At the moment, the only way to make velocity and anellipticity analyses is to use two passes, in particular making use of parabolic approximations of NMO residuals, in order to obtain a dense picking of the V and η parameters.

In this context:

-   -   the first step is to estimate residual velocities, using near         offset data, according to a first estimate of velocities;     -   the next step is to estimate anellipticity on all data, using         velocity updates done previously.

A mute law must also be defined to estimate residual velocities, so as to only keep data that are considered as being near offset data.

However, the efficiency of the two-pass analysis is particularly sensitive to the choice of such a mute law.

On the other hand, the anellipticity η is estimated mainly making use of far offset data.

But, the anellipticity estimate made for far offset data is not very precise, such that the correction made is finally inaccurate.

One purpose of the invention is to overcome these limitations and disadvantages, by proposing a processing including a static NMO correction which is more efficient and more precise.

More precisely, the purpose of the invention is a dense determination of velocity V and anellipticity η parameters in a single pass using all available data, in other words making use of all offset ranges.

To achieve this, the invention proposes a method of determining the velocity V and anellipticity η parameters for processing seismic traces from a common midpoint (CMP) gather including an anelliptic NMO correction, comprising:

-   -   a preliminary step to define a plurality of nodes (dtn, τ₀), the         said nodes being indicative of parameters dtn and τ₀         representing the NMO correction for the maximum offset and the         zero offset travel time in hyperbolic coordinates, the said         preliminary step being followed by     -   for each node (dtn, τ₀) defined in the preliminary step, steps         for the NMO correction of traces in the CMP gather as a function         of the values of the said parameters dtn and τ₀ at the node         considered, and for calculating the semblance function         associated with the said NMO correction for the node considered;         and     -   for each picked time t₀, a step including determination of the         maximum semblance node (dtn(t₀), τ₀ (t₀) )     -   and a final step to convert the dtn(t₀) and τ₀ (t₀) parameters         so as to obtain the velocity V(t₀) and anellepticity η (t₀)         laws.

According to a first embodiment of the invention, the processing done is a static NMO correction of seismic traces.

According to a second embodiment of the invention, the processing done is a PSTM migration of seismic traces, the said PSTM migration including a static PSTM NMO correction of the said seismic traces.

A preferred but non-limitative aspect of the process according to the invention relates to the definition of the dtn and τ₀ parameters relative to the velocity V and the anellipticity η so as to make static NMO corrections, according to ${dtn} = {{\frac{8\quad\eta}{1 + {8\quad\eta}}t_{0}} + \sqrt{\left( \frac{t_{0}}{1 + {8\quad\eta}} \right)^{2} + \frac{x_{\max}^{2}}{\left( {1 + {8\quad\eta}} \right)V^{2}}}}$ and $\tau_{0} = {\frac{t_{0}}{1 + {8\quad\eta}}.}$

Other aspects, purposes and advantages of this invention will become clearer after reading the following detailed description with reference to the attached Figures in which:

FIG. 1 a shows the anelliptic offset hyperbola used to make the NMO correction and illustrates the meaning of the parameters τ₀ and dtn;

FIG. 1 b represents the DSQR equation of the double anelliptic offset hyperbola of the PSTM migration and illustrates the meaning of the τ₀ and dtn parameters;

FIG. 2 illustrates the effect of the τ₀ parameter of the reflection curve corrected by the NMO correction;

FIGS. 3 a and 3 b represent the analysis volume (t₀, dtn, τ₀) in which the bispectral picking of the dtn and τ₀ parameters according to the invention is made;

FIG. 4 combines each of (V, V_(an)) and (dtn, τ₀) approaches, representing their corresponding bispectral analysis panel;

FIG. 5 shows the correspondence between the (dtn, τ₀) and (V, V_(an)) pairs of NMO correction parameters;

FIG. 6 shows a CMP gather of true seismic traces before the NMO correction and the bispectral picking of the (dtn, τ₀) parameters corresponding to this gather of traces;

FIG. 7 shows the semblance function and velocity and anellipticity functions deduced from the picking of the dtn and τ₀ parameters in FIG. 6.

FIG. 8 a is a flowchart representing the steps of a first particular embodiment of the invention, namely determination of the V and η parameters to make an NMO correction;

FIG. 8 b is a flowchart representing the steps of a second particular embodiment of the invention, namely determination of V and η parameters to do a PSTM migration;

FIG. 9 is a diagram illustrating the different operations carried out in order to determine the V and η parameters to make a PSTM migration.

In general, the method according to the invention is a method for processing records of variable offset seismic traces, and this processing uses the recorded seismic traces to build common midpoint (CMP) trace gathers, and the traces in each gather are subjected to an NMO correction.

In particular, the method according to the invention determines the velocity V and anellipticity η parameters to perform processing including such an NMO correction of the seismic traces of a CMP gather.

For example, the said processing may be:

-   -   an anelliptic NMO correction of the seismic traces;     -   an anelliptic PSTM migration which, as we have seen above,         jointly applies TZO and migration operations (in the following         we will refer to a PSTM NMO correction).

The following description is more specifically applicable to the NMO correction. However, considering in particular the two particular embodiments of the invention that will be described below, we can see that this description is equally applicable to any processing including an NMO correction, particularly processing including a PSTM NMO correction.

Two new parameters dtn and τ₀ are considered in order to specifically determine V and η:

-   -   τ₀ that represents the zero offset travel time in “hyperbolic         coordinates” (see FIG. 1), $\begin{matrix}         {\tau_{0} = {\frac{t_{0}}{1 + {8\quad\eta}}\eta}} & {{Equation}\quad(2)}         \end{matrix}$     -    and,     -   dtn that represents the NMO correction for the largest offset         x_(max) (see FIG. 1),         -   dtn=t_(X=Xmax)−t_(x=0) namely: $\begin{matrix}             {{dtn} = {{\frac{8\quad\eta}{1 + {8\quad\eta}}t_{0}} + \sqrt{\left( \frac{t_{0}}{1 + {8\quad\eta}} \right)^{2} + \frac{x_{\max}^{2}}{\left( {1 + {8\quad\eta}} \right)V^{2}}}}} & {{Equation}\quad(3)}             \end{matrix}$

It is important to note that dtn is defined relative to the velocity V and the anellipticity η, while τ₀ is a perfectly anelliptical parameter defined relative to the anellipticity η, independent of V.

Accordingly, the velocity V and anellipticity η parameters may be calculated in accordance with equations (2) and (3), using the following conversion equations (4) and (5): $\begin{matrix} {{V = \frac{x_{\max}}{\sqrt{{{dtn}\left( {{dtn} + {2\quad\tau_{0}}} \right)}\frac{t_{0}}{\tau_{0}}}}}{and}} & {{Equation}\quad(4)} \\ {\eta = {\frac{1}{8}\left( {\frac{t_{0}}{\tau_{0}} - 1} \right)}} & {{Equation}\quad(5)} \end{matrix}$

FIG. 1 a shows the anelliptical offset hyperbola used to make the NMO correction and illustrates the meaning of the τ₀ and dtn parameters.

The said “hyperbolic coordinates” are shown in this FIG. 1. Their origin on the time axis is taken at the intersection of the said time axis with the asymptote tangent to the said far offset offset hyperbola (see equation (1a)).

Using the (dtn, τ₀) parameters, equation (1a) for the anelliptical offset hyperbola becomes: $\begin{matrix} {t = {t_{0} - \tau_{0} + {\sqrt{\tau_{0}^{2} + \frac{{dtn}\left( {{dtn} + {2\quad\tau_{0}}} \right)}{x_{\max}^{2}}}x^{2}}}} & {{Equation}\quad\left( {6a} \right)} \end{matrix}$

The (dtn, τ₀) parameters defined for the velocity V and anellipticity η are thus used to make the NMO correction CORR_(NMO)=t−t₀ to be applied to offset x traces independent of t₀: $\begin{matrix} {{{CORR}_{NMO}(x)} = {{- \tau_{0}} + {\sqrt{\tau_{0}^{2} + \frac{{dtn}\left( {{dtn} + {2\quad\tau_{0}}} \right)}{x_{\max}^{2}}}x^{2}}}} & {{Equation}\quad\left( {7a} \right)} \end{matrix}$

Therefore, this is a static NMO correction. In other words, the data recorded on a given offset trace will all be corrected in the same way for a (dtn, τ₀) pair, independently of the time at which these data were acquired.

Consequently, the estimate of the velocity and anellipticity parameters is not disturbed by stretching of traces usually observed when dynamic NMO corrections are made.

Similarly using the two parameters (dtn, τ₀), equation (1b) for the DSQR double offset hyperbola for the anelliptic PSTM migration becomes: $\begin{matrix} \begin{matrix} {t = {t_{0} - \tau_{0} + \sqrt{\frac{\tau_{0}^{2}}{4} + \frac{{{dtn}\left( {{dtn} + {2\quad\tau_{0}}} \right)}\left( {x - x_{m} + h} \right)^{2}}{x_{\max}^{2}}} +}} \\ {\sqrt{\frac{\tau_{0}^{2}}{4} + \frac{{{dtn}\left( {{dtn} + {2\quad\tau_{0}}} \right)}\left( {x - x_{m} - h} \right)^{2}}{x_{\max}^{2}}}} \end{matrix} & {{Equation}\quad\left( {6b} \right)} \end{matrix}$

FIG. 1 b shows the DSQR double offset hyperbola of the PSTM migration defined with the (dtn, τ₀) parameters.

In the context of the PSTM migration, X_(max) represents the maximum offset and aperture of the migration.

The (dtn, τ₀) parameters defined relative to the velocity V and anellipticity η are thus used to make the PSTM NMO correction CORR_(PSTM)=t−τ₀ to be applied to the offset x traces independent of τ₀ (equation 7b)) $\begin{matrix} {{{Corr}_{PSTM}(x)} = {{- \tau_{0}} + \sqrt{\frac{\tau_{0}^{2}}{4} + \frac{{{dtn}\left( {{dtn} + {2\quad\tau_{0}}} \right)}\left( {x - x + h} \right)^{2}}{x_{\max}^{2}}} +}} \\ {\sqrt{\frac{\tau_{0}^{2}}{4} + \frac{{{dtn}\left( {{dtn} + {2\quad\tau_{0}}} \right)}\left( {x - x - h} \right)^{2}}{x_{\max}^{2}}}} \end{matrix}$

Therefore, this -is a static PSTM correction. In other words, the se of aperture samples x−x_(m) of an “iso-offset” cube are offset by the same time for a given (dtn, τ₀) pair.

By analysing the (dtn, τ₀) parameters in several picking times, the method according to the invention can be used in particular to determine the (V, η) parameters necessary for processing including an anelliptic NMO correction of the traces of a CMP gather.

The said process includes the steps presented below in a simplified manner.

During the preliminary step, an analysis volume is defined including several nodes (dtn, τ₀).

The following are performed for all nodes in this volume:

-   -   firstly, according to equation (7a), the static NMO correction         of traces in the studied CMP gather, as a function of the values         of the dtn, τ₀ parameters at the node considered, the said         static correction being valid for any picking time;     -   secondly, the semblance as a function of time associated with         the correction made in the previous step is calculated.

Finally, the following are determined for each time in the several picking times:

-   -   firstly, the node (dtn, τ₀) used to make an optimum correction,         for example with regard to the semblance criterion (this type of         criterion typically being used in seismic processing to “measure         the horizontality” of reflection curves and to determine the         reliability of the picking);     -   secondly, the values of the dtn, τ₀ parameters at the said         maximum semblance node are converted to values of the velocity V         and anellipticity η parameters at the said picking time         considered.

The velocity law (in other words all (picking time, V)) pairs and the anellipticity law (all (picking time, η)) pairs are thus defined.

Finally, the NMO correction for all seismic traces may be made using these velocity V and anellipticity η laws in equation (1a) for the anelliptic offset hyperbola.

Similarly, and as will be described in detail later, the (dtn, τ₀) parameters of the static PSTM migration (see equation 7b) ) may also be checked. The velocity V and anellipticity η laws are then determined and may be used to make the PSTM migration in the DSQR equation (1b) for the double anelliptic offset hyperbola.

FIG. 2 illustrates the effect of the parameter τ₀ (and therefore the anellipticity η according to equation (2) on the curvature residues after the NMO correction.

Note that the vertical time scale of the curve in FIG. 2 is exaggerated so that this effect can be clearly understood.

Three curves are shown in FIG. 2, for which the dtn parameter is fixed to the correct value and the parameter τ₀ is assigned different values.

The central curve shows the case in which τ₀ is equal to its correct value τ₀₁, in other words when the corresponding anellipticity η₁ is equal to its true value η_(true). As expected, the corrected reflection curve is then horizontal.

The upper curve shows the case in which τ₀ is equal to a value τ₀₂ less than its correct value τ₀₁, the corresponding anellipticity η₂ being greater than its true value η_(true).

The lower curve represents the case in which τ₀ is equal to a value τ₀₃ greater than its true value τ₀₁, the anellipticity η₃ being less than its true value η_(true).

Note that these lower and upper curves show that the “horizontality” of the corrected reflection curve is acceptable at near offset (x≈0) and at far offset (x≈x_(max)).

On the other hand, significant curvature residues are observed when the offset x no longer tends towards one of these limiting values 0 and x_(max). In particular, particularly significant residues are observed for an offset x centred in the middle of the offsets range.

For example, and as is shown in FIG. 2, when τ₀ is equal to τ₀₂, an RMOτ₀₂ residual correction must be made to the offset traces x_(RMO)τ₀₂. Similarly, when τ₀ is equal to τ₀₃, a residual correction RMOτ₀₃ must be made to offset traces X_(RMO)τ₀₃.

Due to these significant curvature residues, the offsets range can be used almost in its entirety in order to determine the anellipticity η.

Therefore, setting parameters in (dtn, τ₀) for the NMO correction make it possible to use available data for all offsets (x between 0 and x_(max)) in determining the anellipticity η.

As has already been mentioned, this is not the case for NMO corrections for which parameters have been set with V and η for which the estimate of the anellipticity η is made essentially using far offset data.

Thus, the effect of the new anelliptic parameter τ₀ is distributed on all offsets, unlike the anellipticity η that only affects far offsets. Therefore, the “behaviour” of the parameter τ₀ gives a better constraint on anellipticity values.

As already mentioned above, the optimum dtn and τ₀ parameters are determined within a 3D analysis volume (t₀, dtn, τ₀).

Several nodes (dtn, τ₀), in other words several pairs of dtn, τ₀ parameters for which values are known, are considered in the said analysis volume.

Nodes are usually regularly spaced from each other, by an increment Δdtn on the dtn axis and an increment Δτ₀ on the τ₀ axis.

Minimum values dtn_(min), τ_(0min), t_(0min) and maximum values dtn_(max), τ_(0max), t_(0max) of the τ₀ and t₀ respectively provide a means of defining the limits of the said analysis volume.

Advantageously, plausible values of the velocity parameter V and the anellipticity parameter η may be used to define a corridor [dtn_(min) (t₀), dtn_(max) (t₀)], [τ_(0min) (t₀), τ_(0max) (t₀)] inside the said analysis volume.

This corridor restricts the analysis volume and therefore the number of nodes (dtn, τ₀) that have to be considered to determine the optimum pair (dtn, τ₀).

Although use of the said corridor is beneficial for the efficiency of the process according to the invention, it also provides a means of constraining solution towards the right phenomena, without needing to consider incompatible (dtn, τ₀) (and therefore V, η) ) pairs, for example related to multiple reflections or miscellaneous interference phenomena.

FIGS. 3 a and 3 b represent the said analysis volume (t₀, dtn, τ₀) in the context of an example of true seismic data processing during an NMO correction done according to the process according to the invention.

FIG. 3 a represents three 2D panels a, b and c of the analysis volume:

-   -   panel a is a panel (dtn, τ₀) with constant t₀;     -   panel b is a panel (dtn, t₀) with constant τ₀;     -   panel c is a panel (τ₀, t₀) with constant dtn.

FIG. 3 b diagrammatically shows the 3D analysis volume (t₀, dtn, τ₀) and three intersections with this volume along three planes with constant t₀, τ₀, dtn respectively, each of these intersections being projected onto the corresponding side a, b or c in FIG. 3 a.

Panels (dtn, τ₀) with constant t₀ (panel a in the above example) are panels in which the bispectral picking of the dtn and τ₀ parameters is made, for example according to the maximum NMO correction semblance criterion, for the considered picking time t₀.

The [dtn_(min) (t₀), dtn_(max) (t₀)] [τ_(0min) (t₀) τ_(0max) (t₀)] corridor mentioned above for the effective analysis inside the analysis volume is also shown in FIG. 3 a (lighter zone on each panel).

The seismic data sampling time step Δt₀ defines the difference between two successive picking times (times for which the maximum associated semblance node (dtn, τ₀) is determined) and therefore the number of bispectral picking panels to be considered.

Automatic picking also provides a means of extracting the dtn, τ₀ parameters at a density that is greater when the Δt₀ increment between picking times is small.

Sampling of the analysis parameters dtn and τ₀ is directly related to the resolution of the seismic exploration; dtn and τ₀ effectively have the same dimensions as seismic records.

The systematic search for the maximum semblance, conventionally known in itself, provides a means of determining the (dtn, τ₀) pair providing best focus, for a given picking time t₀.

Parabolic interpolations about the values of nodes (dtn, τ₀) can also provide a means of evaluating values of the dtn, τ₀ parameters between the different nodes that have actually been picked. And in particular this type of evaluation makes determination even more precise (in contrast to determination limited to nodes in the corridor) of the dtn, τ₀ parameter pair maximising the semblance function.

Finally, the velocity V and anellipticity η parameters are determined, always for the picking time t₀ considered, by using the above mentioned conversion equations (4) and (5).

FIG. 4 shows the comparison between the two approaches (V, V_(an)) and (dtn, τ₀), by representing the bispectral picking panel for each, for a given picking time.

The figure at the right illustrates the conventional approach (V, V_(an)) for which the two axes are the velocity axes (the anellipticity η being related to the ratio of these two velocities according to $\left. {\eta = {\frac{1}{8}\left( {\frac{V_{an}^{4}}{V^{4}} - 1} \right)}} \right).$

The left figure illustrates the approach (dtn, τ₀) according to the invention for which the two axes are time axes.

It is important to note from the study in FIG. 4 that the dtn and τ₀ parameters appear to be decorrelated. This “decorrelation” is striking when the two approaches are compared, spreading of the (dtn, τ₀) spectrum actually being much narrower than spreading of the (V, V_(an)) spectrum.

Therefore the picking made in the context of the (dtn, τ₀) approach according to the invention is more precise than the approach carried out in conventional methods.

Furthermore, this decorrelation enables filtering of the dtn and τ₀ pickings separately, while keeping NMO corrections. This is not the case for the V and η parameters for which a reduction in one of the parameters must necessarily be compensated by an increase in the other and vice versa.

And due to interpolations and individual filtering of parameters according to the invention, dtn and τ₀, it is then possible to perform simultaneous interpolation and filtering of the standard NMO correction parameters V and η.

FIG. 5 shows non-linear correspondence according to equations (4) and (5) mentioned above, between the pair of time parameters (dtn, τ₀) and the pair of velocity parameters (V, V_(an)).

FIG. 6 shows, from left to right:

-   -   a CMP gather of real seismic traces before NMO correction;     -   the picking of the dtn parameter corresponding to this gather of         traces;     -   the picking of the τ₀ parameter corresponding to this gather of         traces.

The straight line τ₀=t₀ on the picking of the parameter τ₀ at the right in FIG. 6, corresponds to the purely hyperbolic reflection curves.

From right to left, FIG. 7 represents the semblance function and the velocity V and the anellipticity η functions (see equation (4) and (5) ) deduced from the picking of the dtn and τ₀ parameters shown in FIG. 6.

On this example of real seismic data processing, it can be seen that the values of V and η obtained generally corresponding to a semblance of more than 40%.

The following description contains details of two particular embodiments of the invention.

The first of these modes relates to a process for determining optimum parameters to make an anelliptic NMO correction to the traces of a CMP gather (see the different steps shown in the flowchart in FIG. 8 a).

With reference to FIG. 8 a, this first embodiment includes an initialisation step 1 a during which the following operations are carried out in sequence:

-   -   determination of the limits of the analysis volume [dtn_(min),         dtn_(max)] [τ_(0min), τ_(0max)] [t_(0min), t_(0max)];     -   calculation of NMO corrections CORR_(NMO) (equation (7a)) for         all offsets and for all nodes (dtn, τ₀) included in the analysis         volume;     -   delimitation inside the analysis volume of the corridor         [dtn_(min) (t₀), dtn_(max) (t₀)] [τ_(0min) (t₀) τ_(0max) (t₀)]         of plausible velocity and anellipticity values.

Once the initialisation step 1 a has been carried out, a step 2 a to calculate velocity V(t₀) and anellipticity η(t₀) laws is performed for each gather of CMP traces.

This step 2 a comprises:

-   -   a first operation 3 a carried out for each node (dtn, τ₀) in the         corridor defined in the initialisation step 1 a, during which         the following operations are carried out in sequence for each         picking time t₀:     -   application of static NMO corrections CORR_(NMO) for all offsets         along the corridor, precalculated during the initialisation step         1 a;         -   calculation of the semblance function on data corrected             along the corridor using a time window appropriate to the             dominant wavelet;         -   summation (“stack” calculation) of data corrected along the             corridor (only near offset data can be used advantageously             for this purpose);     -   a second operation 4 a carried out for each picking time t₀ (the         said times being at intervals of Δt₀ between [t_(0min),         t_(0max)] during which the following operations are carried out:     -   search for maximum semblance in the [dtn_(min) (t₀), dtn_(max)         (t₀))] [τ_(0min) (t₀) τ_(0max) (t₀)] corridor of the bispectral         panel (dtn, τ₀);         -   check the fact that the position in (dtn, τ₀) at the maximum             semblance corresponds to a summation extreme value for the             same values dtn and τ₀;         -   creation of the dtn(t₀), τ₀ (t₀) and semblance (t₀) series;     -   a third operation 5 a designed to select and adjust the pickings         obtained, during which the following operations are carried out:         -   increasing sort of the semblance series (t₀);         -   validation of pickings dtn and τ₀ for which the distance in             time to the highest semblance pickings is greater than a             predefined value;         -   adjustment of picking dtn and τ₀values validated by             parabolic interpolations using surrounding values;         -   retention of picked, validated and adjusted values if it is             possible to calculate the Dix interval velocities with the             pickings with the highest similarities.     -   a fourth operation 6 a designed to use equations (3) and (4) to         convert picked, validated and adjusted and retained values of         dtn and τ₀ during operation 5 a, into velocity V and         anellipticity η laws.

The velocity V and anellipticity η laws as a function of time are thus perfectly determined. The anelliptical NMO correction of seismic traces in the CMP gather can thus be done precisely.

The second particular embodiment of the invention relates to a process for determination of optimum parameters for anelliptical PSTM migration of traces in a CMP gather.

This second embodiment may be included in a generalisation of the first mode discussed above.

As has already been demonstrated, the use of the (dtn, τ₀) parameters enables static PSTM NMO corrections (see equation (7b)).

In the context of a PSTM NMO correction, this application has the same advantages as previously discussed for the NMO obliqueness correction.

More precisely, it will be noted that the first embodiment is only a special case of the second embodiment corresponding to the case of a zero migration aperture.

With reference to FIG. 8 b, the second embodiment includes an initialisation step 1 b during which the following operations are carried out in sequence:

-   -   determine the limits of the analysis volume [dtn_(min),         dtn_(max)], [τ_(0min), τ_(0max)], [t_(0min), t_(0max)];     -   calculate NMO corrections CORR_(PSTM) (equation (7b)) for all         nodes (dtn, τ₀) included in the analysis volume and for all         migration offsets inside the migration aperture;     -   delimitation of plausible velocity and anellipticity values         inside the analysis volume of the corridor [dtn_(min) (t₀),         dtn_(max) (t₀)] [τ_(0min) (t₀) τ_(0max) (t₀)].

Once this initialisation step 1 b has been done, the said first embodiment creates a step 2 b to calculate the velocity V(t₀) and anellipticity η(t₀) laws for each gather of CMP traces.

This step 2 b comprises:

-   -   a first operation 3 b done for each node (dtn, τ₀) of the         corridor defined during the initialisation step 1 a, during         which the following are carried out in sequence:     -   for each offset class, operations for:         -   application on all midpoints inside the migration aperture             along the corridor, of static corrections CORR_(PSTM)             precalculated during the initialisation step 1 b;         -   summation of corrected midpoints along the corridor.     -   for each picking time t₀, operations to:         -   calculate the semblance function on corrected data along the             corridor using a time window appropriate to the dominant             wavelet;         -   summation (stack calculation) of data corrected along the             corridor (only data with small offsets can be used             advantageously for this purpose):     -   a second operation 4 b carried out for each picking time t₀,         similar to the operation 4 a described above, to create the         dtn(t₀), τ₀ (t₀) and semblance t₀ series;     -   a third operation similar to operation 5 b described above,         designed to select and adjust the pickings obtained;     -   a fourth operation 6 b similar to operation 5 a described above,         designed to convert values of dtn, τ₀ into velocity V and         anellipticity η laws.

The velocity V and anellipticity η laws as a function of time are thus perfectly determined. And the PSTM migration of seismic traces in the CMP gather may thus be done accurately.

FIG. 9 illustrates the second embodiment of the invention that has just been described.

Seismic data are initially grouped into iso-offset cubes.

As has just been described, NMO corrections CORR_(PSTM) are applied (see first operation in step 3 b) for each offset class (namely for each iso-offset cube) on all midpoints. The arrow marked with the MIG label in FIG. 9 illustrates this operation.

The midpoints thus corrected are then summated during a second operation in step 3 b, the arrow labelled STACK in FIG. 9 illustrating this operation.

These two MIG and STACK operations are specific to the second embodiment of the invention (PSTM migration).

The following operations are performed in the context of each of the two embodiments discussed (the NMO obliqueness correction, as we have described, corresponding to the special case of a PSTM migration with zero migration aperture).

The semblance is then calculated for each picking time (second operation in step 3 a for the NMO correction only, third operation in step 3 b for the PSTM migration), the arrow labelled “semblance” in FIG. 9 illustrating this operation.

Obviously, the MIG, STACK and semblance calculation operations are implemented for each node (dtn, τ₀).

The “automatic bispectral picking” mentioned in FIG. 9 corresponds to picking of maximum semblance parameters (dtn, τ₀) for each picking time t₀ (operations 4 a, 4 b in FIGS. 8 a, 8 b respectively). The arrow labelled MAX illustrates the search for the maximum semblance.

Finally, the pickings of the picked parameters (dtn, τ₀) are converted into velocity V and anellipticity η laws (operations 6 a, 6 b in FIGS. 8 a, 8 b and arrow labelled CONV in FIG. 9). 

1. Method of determining the velocity v and anellipticity η parameters for processing seismic traces in a common midpoint (CMP) gather including an anelliptic NMO correction, comprising: a preliminary step to define a plurality of nodes (dtn, τ₀), the said nodes being indicative of parameters dtn and τ₀ representing the NMO correction for the maximum offset and the zero offset travel time in hyperbolic coordinates, the said preliminary step being followed by for each node (dtn, τ₀) defined in the preliminary step, the following steps: for static NMO correction of traces in the CMP gather as a function of the values of the said parameters dtn, τ₀ at the node considered, and for calculating the semblance function associated with the said NMO correction for the node considered; and for each picked time t₀, a step including determination of the maximum semblance node (dtn (t₀), τ₀ (t₀)), and a final step to convert the dtn (t₀) and τ₀ (t₀) parameters so as to obtain the velocity V (t₀) and anellepticity η (t₀) laws.
 2. Method according to claim 1, wherein the nodes are defined during the preliminary step in an analysis volume (dtn, τ₀, t₀) determined by minimum and maximum values respectively [dtn_(min), dtn_(max)] [τ_(0min), τ_(0max)] and [t_(0min), t_(0max)] of the dtn, τ₀ and t₀ parameters.
 3. Method according to claim 2, wherein, during the preliminary step, a corridor [dtn_(min) (t₀), dtn_(max) (t₀)], [τ_(0min) (t₀), τ_(0max) (t₀)] for changing dtn and τ₀ parameters is delimited inside the analysis volume as a function of plausible velocity V and anellipticity η values, the nodes (dtn, τ₀) defined for applying the NMO correction being then located along the corridor thus delimited.
 4. Method according to claim 1, further comprising, for each node (dtn, τ₀), a stacking step of the corrected seismic traces, following the semblance function calculation step.
 5. Method according to claim 4, wherein the stacking of corrected traces is done using only near offset traces.
 6. Method according to claim 4, further comprising for each picked time, and following the step for determining the maximum semblance node, a step of checking that values dtn and τ₀ of the maximum semblance node correspond to a stacking extreme value for the same values dtn and τ₀.
 7. Method according to claim 1, further comprising a step of selecting and adjusting the pickings obtained, following the step implemented for determining the maximum semblance node (dtn (t₀), τ₀ (t₀)) for each picked time t₀, before the conversion step.
 8. Method according to claim 7, wherein the said step of selecting and adjusting the pickings comprises a step of only retaining pickings dtn and τ₀ for which time to the highest semblance pickings is greater than a predefined value.
 9. Method according to claim 8, wherein the said step of selecting and adjusting the pickings also comprises a step for adjusting the retained pickings dtn and τ₀ by parabolic interpolations using values about the said picked values.
 10. Method according to claim 9, wherein the said step of selecting and adjusting pickings also comprises a step of eliminating retained and adjusted pickings dtn and τ₀ when it is impossible to calculate the Dix interval velocities between the picking considered and higher semblance pickings.
 11. Method according to claim 1, wherein the processing applied to seismic traces is an NMO correction process implementing a static correction CORR_(NMO).
 12. Method according to claim 11, wherein, during the preliminary step, the NMO corrections CORR_(NMO) are calculated for all nodes (dtn, τ₀) including in the analysis volume and all offsets of processed seismic traces.
 13. Method according to claim 12, wherein the NMO correction carried out for each node (dtn, τ₀), consists of applying NMO corrections CORR_(NMO) calculated during the preliminary step.
 14. Method according to claims 11, wherein for a given (dtn, τ₀) pair, the static NMO correction CORR_(NMO) of a seismic trace with offset x is carried out according to the following equation: ${{CORR}_{NMO}(x)} = {{- \tau_{0}} + {\sqrt{\tau_{0}^{2} + \frac{{dtn}\left( {{dtn} + {2\quad\tau_{0}}} \right)}{x_{\max}^{2}}}x^{2}}}$ in which X_(max) represents the maximum offset in the CMP gather.
 15. Method according to claim 1, wherein the processing applied to seismic traces is a PSTM migration using a static NMO correction CORR_(PSTM).
 16. Method according to claim 15, wherein, during the preliminary step, the NMO corrections CORR_(PSTM) are calculated for all nodes (dtn and τ₀) included in the analysis volume and all migration offsets inside the migration aperture.
 17. Method according to claim 16, wherein the NMO correction step carried out for each node (dtn and τ₀) comprises, for each offset class, application of the said NMO corrections CORR_(PSTM), calculated during the preliminary step on all midpoints inside the migration aperture.
 18. Method according to claim 17, wherein the NMO correction step carried out for each node (dtn and τ₀) comprises, for each offset class, the stack of the corrected midpoints following application of the said NMO corrections CORR_(PSTM).
 19. Method according to claim 15, wherein, for a given pair (dtn and τ₀), the static NMO correction CORR_(PSTM) is carried out according to the following equation: $\begin{matrix} {{{CORR}_{PSTM}(x)} = {{- \tau_{0}} + \sqrt{\frac{\tau_{0}^{2}}{4} + \frac{{{dtn}\left( {{dtn} + {2\quad\tau_{0}}} \right)}\left( {x - x + h} \right)^{2}}{x_{\max}^{2}}} +}} \\ {\sqrt{\frac{\tau_{0}^{2}}{4}} + \frac{{{dtn}\left( {{dtn} + {2\quad\tau_{0}}} \right)}\left( {x - x - h} \right)^{2}}{x_{\max}^{2}}} \end{matrix}$ where: x_(m) represents the coordinates of the midpoints, x−x_(m) represents the migration aperture PSTM, h is the half source—receiver offset, xmax is the maximum offset and aperture of the migration.
 20. Method according to claim 14, wherein, during the final conversion step, the parameters dtn (t₀) and (τ₀) are converted to the velocity law v (t₀) according to the following equation: $V = \frac{x_{\max}}{\sqrt{{{dtn}\left( {{dtn} + {2\quad\tau_{0}}} \right)}\frac{t_{0}}{\tau_{0}}}}$
 21. Method according to claim 14, wherein, during the final conversion step, the parameter τ₀ (t₀) is converted to the anellepticity η (t₀) law according to $\eta = {\frac{1}{8}\left( {\frac{t_{0}}{\tau_{0}} - 1} \right)}$
 22. Method according to claim 20, wherein parameter dtn is defined with respect to the velocity v and anellepticity η according to the following equation: ${dtn} = {{\frac{8\quad\eta}{1 + {8\quad\eta}}t_{0}} + \sqrt{\left( \frac{t_{0}}{1 + {8\quad\eta}} \right)^{2} + \frac{x_{\max}^{2}}{\left( {1 + {8\quad\eta}} \right)V^{2}}}}$
 23. Method according to claim 21, wherein parameter τ₀ is defined according to anellepticity η according to the following equation: $\tau_{0} = \frac{t_{0}}{1 + {8\quad\eta}}$
 24. Method of characterizing a velocity field for processing seismic data using a gather of seismic traces at common midpoint, wherein, for each travel time t₀ for a zero offset, a set of parameters dtn and τ₀ is defined, representing the NMO correction for maximum offset, and the zero offset travel time respectively, in hyperbolic coordinates.
 25. Method according to claim 2, further comprising, for each node (dtn, τ₀), a stacking step of the corrected seismic traces, following the semblance function calculation step.
 26. Method according to claim 25, wherein the stacking of corrected traces is done using only near offset traces.
 27. Method according to claim 25, further comprising for each picked time, and following the step for determining the maximum semblance node, a step of checking that values dtn and τ₀ of the maximum semblance node correspond to a stacking extreme value for the same values dtn and τ₀.
 28. Method according to claim 2, further comprising a step of selecting and adjusting the pickings obtained, following the step implemented for determining the maximum semblance node (dtn (t₀), τ₀ (t₀)) for each picked time t₀, before the conversion step.
 29. Method according to claim 28, wherein the said step of selecting and adjusting the pickings comprises a step of only retaining pickings dtn and τ₀ for which time to the highest semblance pickings is greater than a predefined value.
 30. Method according to claim 29, wherein the said step of selecting and adjusting the pickings also comprises a step for adjusting the retained pickings dtn and τ₀ by parabolic interpolations using values about the said picked values.
 31. Method according to claim 30, wherein the said step of selecting and adjusting pickings also comprises a step of eliminating retained and adjusted pickings dtn and τ₀ when it is impossible to calculate the Dix interval velocities between the picking considered and higher semblance pickings.
 32. Method according to claim 2, wherein the processing applied to seismic traces is an NMO correction process implementing a static correction CORR_(NMO).
 33. Method according to claim 32, wherein, during the preliminary step, the NMO corrections CORR_(NMO) are calculated for all nodes (dtn, τ₀) including in the analysis volume and all offsets of processed seismic traces.
 34. Method according to claim 32, wherein the NMO correction carried out for each node (dtn, τ₀ ), consists of applying NMO corrections CORR_(NMO) calculated during the preliminary step.
 35. Method according to claim 32, wherein for a given (dtn, τ₀) pair, the static NMO correction CORR_(NMO) of a seismic trace with offset x is carried out according to the following equation: ${{CORR}_{NMO}(x)} = {{- \tau_{0}} + {\sqrt{\tau_{0}^{2} + \frac{{dtn}\left( {{dtn} + {2\quad\tau_{0}}} \right)}{x_{\max}^{2}}}x^{2}}}$ in which X_(max) represents the maximum offset in the CMP gather.
 36. Method according to claim 2, wherein the processing applied to seismic traces is a PSTM migration using a static NMO correction CORR_(PSTM).
 37. Method according to claim 36, wherein, during the preliminary step, the NMO corrections CORR_(PSTM) are calculated for all nodes (dtn and τ₀) included in the analysis volume and all migration offsets inside the migration aperture.
 38. Method according to claim 37, wherein the NMO correction step carried out for each node (dtn and τ₀) comprises, for each offset class, application of the said NMO corrections CORR_(PSTM), calculated during the preliminary step on all midpoints inside the migration aperture.
 39. Method according to claim 38, wherein the NMO correction step carried out for each node (dtn and τ₀) comprises, for each offset class, the stack of the corrected midpoints following application of the said NMO corrections CORR_(PSTM).
 40. Method according to claim 36, wherein, for a given pair (dtn and τ₀), the static NMO correction CORR_(PSTM) is carried out according to the following equation: $\begin{matrix} {{{CORR}_{PSTM}(x)} = {{- \tau_{0}} + \sqrt{\frac{\tau_{0}^{2}}{4} + \frac{{{dtn}\left( {{dtn} + {2\quad\tau_{0}}} \right)}\left( {x - x + h} \right)^{2}}{x_{\max}^{2}}} +}} \\ {\sqrt{\frac{\tau_{0}^{2}}{4}} + \frac{{{dtn}\left( {{dtn} + {2\quad\tau_{0}}} \right)}\left( {x - x - h} \right)^{2}}{x_{\max}^{2}}} \end{matrix}$ where: x_(m) represents the coordinates of the midpoints, x−x_(m) represents the migration aperture PSTM, h is the half source—receiver offset, xmax is the maximum offset and aperture of the migration.
 41. Method according to claim 35, wherein, during the final conversion step, the parameters dtn (t₀) and (τ₀) are converted to the velocity law v (t₀) according to the following equation: $V = \frac{x_{\max}}{\sqrt{{{dtn}\left( {{dtn} + {2\quad\tau_{0}}} \right)}\frac{t_{0}}{\tau_{0}}}}$
 42. Method according to claim 35, wherein, during the final conversion step, the parameter τ₀ (t₀) is converted to the anellepticity η (t₀) law according to $\eta = {\frac{1}{8}\left( {\frac{t_{0}}{\tau_{0}} - 1} \right)}$
 43. Method according to claim 41, wherein parameter dtn is defined with respect to the velocity v and anellepticity η according to the following equation: ${dtn} = {{\frac{8\quad\eta}{1 + {8\quad\eta}}t_{0}} + \sqrt{\left( \frac{t_{0}}{1 + {8\quad\eta}} \right)^{2} + \frac{x_{\max}^{2}}{\left( {1 + {8\quad\eta}} \right)V^{2}}}}$
 44. Method according to claim 42, wherein parameter τ₀ is defined according to anellepticity η according to the following equation: $\tau_{0} = \frac{t_{0}}{1 + {8\quad\eta}}$
 45. Method according to claim 3, further comprising, for each node (dtn, τ₀), a stacking step of the corrected seismic traces, following the semblance function calculation step.
 46. Method according to claim 45, wherein the stacking of corrected traces is done using only near offset traces.
 47. Method according to claim 45, further comprising for each picked time, and following the step for determining the maximum semblance node, a step of checking that values dtn and τ₀ of the maximum semblance node correspond to a stacking extreme value for the same values dtn and τ₀.
 48. Method according to claim 3, further comprising a step of selecting and adjusting the pickings obtained, following the step implemented for determining the maximum semblance node (dtn (t₀), τ₀ (t₀)) for each picked time t₀, before the conversion step.
 49. Method according to claim 48, wherein the said step of selecting and adjusting the pickings comprises a step of only retaining pickings dtn and τ₀ for which time to the highest semblance pickings is greater than a predefined value.
 50. Method according to claim 49, wherein the said step of selecting and adjusting the pickings also comprises a step for adjusting the retained pickings dtn and τ₀ by parabolic interpolations using values about the said picked values.
 51. Method according to claim 50, wherein the said step of selecting and adjusting pickings also comprises a step of eliminating retained and adjusted pickings dtn and τ₀ when it is impossible to calculate the Dix interval velocities between the picking considered and higher semblance pickings. 